This paper presents a new constructive model predictive control approach to asymptotic stabilization of constrained, discrete time-invariant nonlinear dynamic systems. The constructive approach not only considers the traditional optimality problem on a finite horizon, but also considers a feasibility constraint imposed at the end of each finite horizon (prediction horizon). The feasibility constraint is included in the optimization formulation as a set of inequality constraints. Sufficient conditions for establishing asymptotic stability of discrete nonlinear systems are derived from the simultaneous solutions of the optimality and the feasibility problems on the finite horizon. The proposed approach is appealing in the sense that no necessary conditions regarding stabilizability of the linearization of the nonlinear dynamic system around an equilibrium, or the identification of an a priory stabilizing control law in a neighborhood of the equilibrium are needed; known as common requirements in many nonlinear model predictive control formulations. Simulation examples for the proposed approach are presented.